A roller-coaster car with a mass of 500 kg starts at rest from point A, which is 20 m above the ground. At point B, it is 10 m above the ground.
(a) What is the initial potential energy of the car?
(b) What is the potential energy at point B?
(c) If the initial kinetic energy was zero and the work done against friction between the starting point A and point B is 12 000 J, what is the kinetic energy of the car at point B?
I've tried forever to figure this one out and its really bothering me :O. Lol, I realize that PE=W*G*H, but in this situation that doesn't seem to work. If you answer PLEASE explain how you got it. Thanks!
(a) What is the initial potential energy of the car?
(b) What is the potential energy at point B?
(c) If the initial kinetic energy was zero and the work done against friction between the starting point A and point B is 12 000 J, what is the kinetic energy of the car at point B?
I've tried forever to figure this one out and its really bothering me :O. Lol, I realize that PE=W*G*H, but in this situation that doesn't seem to work. If you answer PLEASE explain how you got it. Thanks!
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(a) Initially, the car has no kinetic energy (it is "at rest"); it only has gravitational potential energy. Thus, the total potential energy at this point is mgh = (500 kg)(9.81 m/s²)(20 m) = 98.1 kN.
(b) At point B, some of the gravitational potential energy would have been converted into kinetic energy (and is therefore no longer potential energy).
Because the cart is now only 10 m above the ground, it's potential energy is only mgh = (500 kg)(9.81 m/s²)(10 m) = 49.05 kN.
(c) The difference between the potential energies at point A and point B must be equal to the carts kinetic energy plus the energy done against friction (can you see why?). Thus:
⌂P.E. = K.E. + W_f
where W_f denotes the work done by friction. Solving for K.E. and substitution yields:
K.E. = ⌂P.E. - W_f = (98,100 N - 49,050 N) - 12,000 J = 37,050 N = 37.05 kN.
(b) At point B, some of the gravitational potential energy would have been converted into kinetic energy (and is therefore no longer potential energy).
Because the cart is now only 10 m above the ground, it's potential energy is only mgh = (500 kg)(9.81 m/s²)(10 m) = 49.05 kN.
(c) The difference between the potential energies at point A and point B must be equal to the carts kinetic energy plus the energy done against friction (can you see why?). Thus:
⌂P.E. = K.E. + W_f
where W_f denotes the work done by friction. Solving for K.E. and substitution yields:
K.E. = ⌂P.E. - W_f = (98,100 N - 49,050 N) - 12,000 J = 37,050 N = 37.05 kN.